Vortex knots in a Bose-Einstein condensate

TL;DR

This paper introduces a numerical method to create and analyze vortex knots in Bose-Einstein condensates, studying their dynamics, stability, and breakup into vortex rings through simulations of the Gross-Pitaevskii equation.

Contribution

It presents a novel numerical approach to construct vortex knots in BECs and investigates their evolution, stability, and breakup mechanisms.

Findings

Vortex knot velocity depends on poloidal and toroidal radius ratio.

Smaller ratio results in faster vortex knot movement.

Unstable vortex knots disintegrate into vortex rings.

Abstract

We present a method for numerically building a vortex knot state in the superfluid wave-function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and stability of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how unstable vortex knots break up into vortex rings.